## Stijn Cambie - Five results on maximizing topological indices in graphs

dmtcs:6896 - Discrete Mathematics & Theoretical Computer Science, November 15, 2021, vol. 23, no. 3 - https://doi.org/10.46298/dmtcs.6896
Five results on maximizing topological indices in graphs

Authors: Stijn Cambie

In this paper, we prove a collection of results on graphical indices. We determine the extremal graphs attaining the maximal generalized Wiener index (e.g. the hyper-Wiener index) among all graphs with given matching number or independence number. This generalizes some work of Dankelmann, as well as some work of Chung. We also show alternative proofs for two recents results on maximizing the Wiener index and external Wiener index by deriving it from earlier results. We end with proving two conjectures. We prove that the maximum for the difference of the Wiener index and the eccentricity is attained by the path if the order $n$ is at least $9$ and that the maximum weighted Szeged index of graphs of given order is attained by the balanced complete bipartite graphs.

Volume: vol. 23, no. 3
Section: Graph Theory
Published on: November 15, 2021
Accepted on: September 29, 2021
Submitted on: November 11, 2020
Keywords: Mathematics - Combinatorics,05C09